Template:Bounds on Time FMB ED: Difference between revisions

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(Created page with '====Bounds on Time==== The bounds around time for a given exponential percentile, or reliability value, are estimated by first solving the reliability equation with respect to t…')
 
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====Bounds on Time====
#REDIRECT [[The Exponential Distribution]]
 
The bounds around time for a given exponential percentile, or reliability value, are estimated by first solving the reliability equation with respect to time, or reliable life:
 
 
::<math>\hat{T}=-\frac{1}{{\hat{\lambda }}}\cdot \ln (R)+\hat{\gamma }</math>
 
 
The corresponding confidence bounds are estimated from:
 
 
::<math>\begin{align}
  & {{T}_{U}}= & -\frac{1}{{{\lambda }_{L}}}\cdot \ln (R)+\hat{\gamma } \\
& {{T}_{L}}= & -\frac{1}{{{\lambda }_{U}}}\cdot \ln (R)+\hat{\gamma } 
\end{align}</math>
 
 
The same equations apply for the one-parameter exponential with <math>\gamma =0.</math>

Latest revision as of 06:52, 10 August 2012

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